ODE solvers for use with the method of lines
The numerical method of lines for time-dependent PDE's or PDE systems requires effective and flexible solvers for systems of ordinary differential equations (initial value problem). The ODE system can be explicit or implicit in form, and is typically large, complex and stiff. Various solvers have been written and used in this context, most using the BDF (Backward Differentiation Formula) methods first introduced in software form by C.W. Gear. Recently, two new solvers have been developed and released, in which flexibility, portability, and ease of use (both generally and for method of lines applications) were prime design criteria: LSODE solves explicit systems y = f(t,y), and LSODI solves linearly implicit systems A(t,y) y = g(t,y), where A is a square matrix. These solvers are described briefly here, and their uses illustrated by example PDE problems.
- Research Organization:
- Lawrence Livermore National Lab., CA (USA)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 6519060
- Report Number(s):
- UCRL-85293(Rev.1); CONF-810628-1(Rev.1)
- Resource Relation:
- Conference: IMACS symposium on computer methods for PDE's, Bethlehem, PA, USA, 30 Jun 1981
- Country of Publication:
- United States
- Language:
- English
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